Ilya Prigogine |

We know Einstein
believed that the passage of time is an illusion. In a letter of condolence he
wrote in 1955 he said:

**. To assert this, he relied on the fact that Newton’s equations of gravitation, his own equations of General Relativity, Maxwell’s equations (which apply to electromagnetic waves) and SchrÃ¶dinger’s equation (which gives the wave function of a particle in quantum mechanics) are all symmetric with respect to time.***...the distinction between past, present and future is only a stubbornly persistent illusion***Usually, physicists who believe that time is an illusion explain it by saying that, at the microscopic level, time is actually reversible, but**

*How then can we explain the fact that it seems so obvious that time goes from the past to the future?***, one of which is the irreversibility of time. Let's give an example:**

*when we move to the macroscopic level, new, emerging phenomena appear*

*According to the usual theories, the movement of the molecules of a gas is perfectly reversible.*

*If we reverse the direction of time, all the particles behave exactly the same and continue colliding with each other, only they would move in the opposite direction. However, when we consider all the trillions of particles that make up a gas, we see irreversible phenomena arising, such as the fact that the gas always tends to occupy as much space as possible, while its accumulation in a corner of the container is much less likely.*
The problem is that
our physical theories are based on approximations. Mathematics is a very
important tool for physics, but in mathematics there are several kinds of very
different problems, which differ in their difficulty to be solved. Let us look
at a few:

: the first, much simpler, can be described by linear equations with the following property:*Linear and non-linear systems*

: the first are differential equations that can be solved into analytical solutions, expressible by means of relatively simple expressions. The latter cannot be integrated analytically, only approximately, by numerical calculation. For example, Einstein’s cosmological equation of General Relativity, which we have seen in several previous posts, can be easily integrated if either its second or its third term is equal to zero, but not if both are different from zero.*Integrable and non-integrable equations*: where you can define an internal scalar product*Hilbert spaces*whose norm, defined below, is complete.

To simplify the
calculations, physicists use to prefer linear to non-linear equations; integrable
to non-integrable equations; and Hilbert spaces (which are used in the
mathematical formulation of quantum mechanics) to spaces not in that
class.

Given this
situation, the Nobel Prize winner Ilya Prigogine (1917-2003), specialist in
dealing with complex dynamic systems far from the equilibrium (such as living
systems), raised the following question:

*Perhaps the apparent reversibility of time at the microscopic level is just a consequence of the simplifications we make in mathematical physics, rather than a real phenomenon.*Albert Einstein |

Put in another way:
is time an illusion, as Einstein believed, or is time really irreversible, and

**?***the illusion of its reversibility is due to the simplification introduced by our mathematical representations*
To answer this
question, Prigogine and his team investigated what would happen if quantum
mechanics (the SchrÃ¶dinger equation) were extended to spaces more complex than
Hilbert space. The result was that time became irreversible. Something similar
happened when classical mechanics and General Relativity were tackled with
non-integrable equations. Finally, even statistical mechanics (the study of the
behavior of gases at the microscopic level) showed a unidirectional time when
the equations were made more complicated. The solutions found, rather than representing
wave functions (for example) turned into intrinsic probability distributions.

Prigogine comes to
the following conclusion:

**. Let us look at his own words:***saying that time is an illusion, is a simplification introduced by our equations***(Prigogine & Antoniou, Laws of Nature and Time Symmetry Breaking, in Tempos in Science and Nature, Annals of the New York Academy of Sciences, Vol. 879, 1999).**

*The inclusion of irreversibility changes our view of nature. The future is no longer given. Our world is a world of continuous “construction” ruled by probabilistic laws and no longer a kind of automaton. We go from a world of "being" to a world of "becoming". Nevertheless, why nature has a broken time symmetry is a difficult question. It may be due to the interaction between gravitation and the other fundamental forces. But at this point we are at the frontiers of present science.***The same post in Spanish**

Thematic thread on Time: Preceding Next

**Manuel Alfonseca**

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